ΤΡΑΠΕΖΑ ΘΕΜΑΤΩΝ - ΑΛΓΕΒΡΑ 4ο ΘΕΜΑ

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2014 4

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  • 1. 2014 4

2. < 3. 4. 5. ),( 21 xxd 24),( 21 =xxd 6. f 2 9 2 )( x x xf + = f D f D f D 7. ^ W ( 8. s 9. 10. BA tt3 2 BA tt t + = = tttt BA 2 BA tt t + = 6=+ BA tt 8= BA tt 11. ( ) = ( ) ( ) = + ( )+ = + + 12. ( ) = 13. 14. 15. ( ) ( )2 2 2 1 . 1 0x x + = 16. s 17. 18. 19. 2 2 x 1 = + 1 2| x x | 1 20. ^ W E 1 2d(x , 1) d(x , 1) 4 = 21. 22. 23. 24. 25. 26. 273 8,1 32 + = F K 27. 28. || 2 21 + 29. || 2 21 + 30. || 31. || +||= 32. || || ||+|| ||+|| 33. || ||. ||=|| 34. 1 ( ) = + ( ) = ( ) ( ) ( ) ( ) = 35. 1 + + = = = + 36. 1 37. 1 + = ^ = + W = + 38. 1 D + ( ) + + = ( ) ( ) + 39. 1 ( ) = + ( ) = + ( ) 40. d 41. 42. a D aa ++ 11 D 43. 3 65 )( 2 + = x xx xf 44. . . 1 A S P = ^ W 45. -{ } -{ ^ W 1 2 1 2x x 2x x+ 1 2x , x 46. 0 4 0 47. | - |= - 48. a D 2 2 aa + D 49. 50. 51. . 52. ( ) = + + = + ( )D = + 53. f + + = 0x,2 0x,2 )( x x xf f yy' 3=y E =y ay = 54. 5 || 2 2 1 1 2 x 5 x 2 0 x x + + + = 55. 56. ^ W D 57. ( ) + = ( )( ) = 58. 59. 60. 2 f(x) x x 4 = + 1 0, 2 1 f(x) 2 = 61. 21 x,x 1 20 d(x , x ) 2 62. 1 2 21 x,x 1 2 1 2 1 d(x ,x ) d(x ,x ) = 63. . 2 2 f (x) x x= + . 64. 2 2 2 (x 1)(x 4) x x + + D 65. 1 2 1 2x x 1 2 1 2 x x x x 2 + 1 2 2 2 x x f (x ), f , f (x 1) 2 + + 66. 2 2 2 (x 1)(x 4) x x + + D D D 67. 68. -{ -{ f (x) 0 69. 1 + = + = + = 70. 1 1 2x 4x 4+ 71. ^ W 72. 2 2 2 x ( )x 0 + + = 2 2 2 ( ) 1 x = 2 x = 1 2(1 x )(1 x ) 4+ + 73. 74. 75. 76. ( ) + = + ( ) = + 77. | | 3 2 3 1 +x )2(23 += xxK 78. -{} 79. 80. 81. D D 82. f(x) 2 2 83. -{ -{ ^ W 0 0 1 2x , x 1 2 1 2 x x x x 2 + 84. -{ -{ ^ W 0 0 1 1 2x , x 1 2x x 2 + 85. -{ -{ ^ W 0 0 1 1 2x , x 1 2x x f (0) f ( ) f ( ) 1 2x x 86. 1 87. 88. 89. 90. 1 + = + = + + 91. = 92. E 93. 4444 8889 94. ^ ^ 95. 96. 97. 98. 99. 4 1 3 1 s 100. 2x2)x(f + 101. 102. 103. 104. 2 1 x 4 x 16 0, (0,4) + + = 16 (0,4) 105. 1 106. 0652 xx 6 47 46 5 47 46 2 + 652 = aa 107. 10yx =+ )10,0(x),x10x( 2 1 )x(E 2 += 2 25 )( xE )10,0(x 2 25 108. Z zKt y ( )f x Z ( )f x ( )g x zKt ( )g x ,f g ( )f x ( )g x ,f g Z Z 109. 2 E 2x 6x 9, x (0,3)= + 9 E , x (0,3) 2 2 9 D 110. i) ii) 111. ^ ^ ^ 112. ^ W 10 113. 114. 2 2 x + 5, x + x, 2x + 4 ^ 115. ^ 116. = 117. 23)( 2 ++= xxxf 1xg(x) += gf , xg(x) += gf , gf , 118. 4 3 BA ss + | | | - | 119. 120. 121. 32 yx = 122. + = + = = + = 123. ( ) = ( ) = + = = = 124. 125. 126. 127. 128. 129. | | )( )(1 xf xf 130. 1 ( )( ) 131. D 1 132. 2 5 2 3 133. 10110021 = 134. 4 1 4 1 135. a 1 ^ ^ 10910 2 1 SS = 136. 2 1 2 1 2 3 137. 1 4 x 4 2x . 10) x i) 4. 5) ii) 3x 138. 1 4 2 3 2x x x 10 2 2 3 2 3 2 0 . 1 2 1 2 . 15 139. 2 x 5x 6 f x 2 x . f . ( x 3, x 2 f x x 3, x 2 . f f x x y y . ( 8 f x 0 ( 140. 2 . f . f. 8 f 1, 1 . 7 f y y . 141. , 2 1 1 3 . ( . 5 2 3 . ( 7 . ( 142. , 1 3 2 1 1 3 . ( 3 1 3. 10 2 2 ( 10 143. * 1 x 2 2 2 3 x 2 x . x 3 . ( 0 - . 8 1 5 15 . ( 7